PHILADELPHIA -- Lisa McHale wishes her husband had lived long enough to learn more about the links between concussions and long-term brain injuries.

Her husband Tom, an All-Ivy athlete who played in 87 NFL games from 1987 to 1995, died of an overdose in 2008 after battling depression and a painkiller addiction. An autopsy later showed he suffered from traumatic brain injuries. But she said it helps that more players now go public with their neurological problems, including some of the thousands now suing the NFL over concussions.

"To know it wasn't his fault, that there was something going on neurologically, it helps," McHale said in Philadelphia on Tuesday, where lawyers for the NFL and for more than 4,200 former players argued over whether the complaints belong in federal court or, as the NFL believes, in arbitration.

A lawyer for the former players argued that the NFL "glorified" violence and profited from damaging hits to the head.

Players' lawyer David Frederick also accused the league of concealing the emerging science linking concussions to neurological problems for decades, even after the NFL created a Mild Traumatic Brain Injury committee in 1994. The panel was led by a rheumatologist.

"It set up a sham committee designed to get information about neurological risks, but in fact spread misinformation," Frederick argued at the pivotal federal hearing to determine if the complaints will remain in federal court.

U.S. District Judge Anita Brody's decision could be worth billions to either side.

About one-third of the league's 12,000 former players have joined the litigation. Some are battling dementia, depression or Alzheimer's disease, and fault the league for rushing them back on the field after concussions. Others are worried about future problems and want their health monitored.

A handful, including popular Pro Bowler Junior Seau, have committed suicide.

NFL lawyer Paul Clement insisted that teams bear the chief responsibility for health and safety under the players' collective bargaining agreement, along with the players and their union.

"The clubs are the ones who had doctors on the sidelines who had primary responsibility for sending players back into the game," Clement said at a news conference after the court hearing.

Brody appeared most interested in whether the contract specifies that head injuries are workplace safety issues that belong in arbitration.

"It has to be really specific. That's what I have to wrestle with," she said.

Frederick called the contract "silent" on latent head injuries, and said players therefore have the right to seek damages in court.

Brody is not expected to rule for several months, and the case could take years to play out if her ruling is appealed, as expected.

Players and relatives on hand for the hearing included Kevin Turner, a former Philadelphia Eagles running back now battling Lou Gehrig's disease; Dorsey Levens, a veteran running back who made a 2012 documentary on concussions called "Bell Rung" and Mary Ann Easterling, whose husband, former Atlanta safety Ray Easterling, was the lead plaintiff in the litigation before he committed suicide last year.

"There are people who aren't going to be able to be around long enough to find out the end of this case, and my husband is one of them," said Eleanor Perfetto, widow of guard Ralph Wenzel, who played for Pittsburgh and San Diego from 1966 to 1973. "He died last June, and I'm here for him. He was sick for almost two decades and, in the end, had very, very severe, debilitating dementia."

One wrinkle in the litigation is what the NFL calls the "gap year" players, who played from 1987 to 1993, when there was no collective bargaining agreement in place. The NFL, eager to avoid opening up its files in legal discovery, argues that those players were bound by previous contracts or contracts later in effect when they collected pensions.

"I certainly admit that the gap year players ... are the most difficult cases," said Clement. But he said very few people played only those years, and not under a contract before or after.

For the latter group, "there's no way to say the only hits that hurt you are the hits from those years," he said.

Tom McHale left behind three sons, who are now teenagers. They do not play football, said his widow, who lives in Tampa, Fla.